Financial Risk Manager Part 1

The correct answer is D because the t-statistic actually has fatter tails than the normal distribution, not thinner tails. This is due to the t-distribution having more probability in its tails compared to the normal distribution.

Explanation of other options:

• Option A is correct: As the degree of freedom increases, the t-statistic approaches the normal distribution, but the statement that it decreases is accurate in the context of how the t-distribution changes with degrees of freedom.
• Option B is correct: A 90% confidence interval with n-1 degrees of freedom is indeed calculated at α/2 or t₀.₀₅, where α = 0.10 for a 90% confidence level.
• Option C is correct: The t-statistic is commonly used for sample sizes smaller than 30 observations, while the z-statistic is typically used for larger sample sizes (n ≥ 30).

Key concept: The t-distribution has fatter tails than the normal distribution, which accounts for the additional uncertainty when working with small sample sizes. As sample size increases (degrees of freedom increase), the t-distribution converges to the normal distribution.